Fuzzy Malliavin derivative and linear Skorohod fuzzy stochastic differential equation

摘要

We extend the definitions of the Gaussian Malliavin calculus operators to fuzzy stochastic processes. We consider Skorohod fuzzy stochastic differential equations, which the integrands of the stochastic integrals are not adapted to the filtration generated by a Wiener process. Such equations with randomness, fuzziness and non-adapted processes can be applied in financial models. We apply the fuzzy Malliavin derivative and related topics to discuss the existence and uniqueness of solutions.